One may not cause an object to become unsuitable for its normal usage (levatel kli me-heikhano) on Shabbat. Doing so is akin to demolishing something (Soter) on Shabbat. Therefore, if oil is dripping from a lamp, one may not put a container underneath it to collect the oil. Since the lamp and its oil are muktzeh, the container will become forbidden to move, and thus it will no longer be fit for normal use on Shabbat. If one wants to ensure that the dripping oil does not make a mess, he should put something under it before Shabbat. Similarly, one may not put a container under a chicken in which it can lay its eggs. Since an egg laid on Shabbat is muktzeh, the container with an egg in it will become forbidden to move (Shabbat 42b; SA 310:6, 265:3).
However, there is a way around this problem. Before placing the receptacle beneath the lamp or the chicken, one may place an item that is more important than the oil or egg. One may then move the container for the sake of that non-muktzeh item (MB 265:6).
If one is worried about sparks flying from a lamp, he may put a kli underneath it to collect the sparks. Because sparks are insubstantial and go out almost immediately, the kli may subsequently be moved. It is not rendered unsuitable for its normal use. However, he should not put water into the kli, because that will extinguish the sparks more quickly (Shabbat 47b; SA 265:4).
Making pillows and blankets wet is forbidden, because doing so makes them unsuitable for their normal use (SA 305:19). It is also forbidden to make an item of clothing so dirty that it is no longer wearable without washing. If liquid spilled on the floor, one may not use clothing to mop it up; by doing so, one is making the clothing unfit to wear. However, one may use a rag to mop up the spill, since this is the intended use of the rag. It is also permissible for many people to dry their hands on a towel, even if it will eventually become too wet to use any longer. This is because they are not making it unusable; rather, they are using it for its intended purpose. Similarly, one may put a garbage bag into a garbage can on Shabbat and put garbage in it, even though doing so gives the bag the muktzeh status of the garbage inside it. This is not considered rendering it unusable, as holding garbage is the purpose of the garbage bag (Levush 265:3; Shulĥan Shlomo 308:17:7; Yalkut Yosef vol. 2, p. 480; Orĥot Shabbat 2:19:329).
One may place a box in front of chicks as a step stool so that they can go back and forth from their coop. Even though animals are muktzeh, this is not considered making the box unusable, since he can shoo the chicks away from it whenever he wants. However, while they are on the box, he may not move it (Shabbat 128b; SA 308:39).